# Mechanical Engineering - GATE 2019 Paper Solution

John Thomas, an __________________ writer, passed away in 2018.

____ I permitted him to leave, I wouldn’t have had any problem with him being absent, _____ I?

A worker noticed that the hour hand on the factory clock had moved by 225 degrees during her stay at the factory. For how long did she stay in the factory ?

The sum and product of two integers are 26 and 165 respectively. The difference between these two integers is _____.

The minister avoided any mention of the issue of women’s reservation in the private sector. He was accused of __________ the issue.

Under a certain legal system, prisoners are allowed to make one statement. If their statement turns out to be true then they are hanged. If the statement turns out to be false then they are shot. One prisoner made a statement and the judge had no option but to set him free. Which one of the following could be that statement ?

A person divided an amount of Rs. 100,000 into two parts and invested in two different schemes. In one he got 10% profit and in the other he got 12%. If the profit percentages are interchanged with these investments he would have got Rs.120 less. Find the ratio between his investments in the two schemes.

Congo was named by Europeans. Congo’s dictator Mobuto later changed the name of the country and the river to Zaire with the objective of Africanising names of persons and spaces. However, the name Zaire was a Portuguese alteration of Nzadi o Nzere, a local African term meaning ‘River that swallows Rivers’. Zaire was the Portuguese name for the Congo river in the 16th and 17th centuries.

Which one of the following statements can be inferred from the paragraph above?

A firm hires employees at five different skill levels P, Q, R, S, T. The shares of employment at these skill levels of total employment in 2010 is given in the pie chart as shown. There were a total of 600 employees in 2010 and the total employment increased by 15% from 2010 to 2016. The total employment at skill levels P, Q and R remained unchanged during this period. If the employment at skill level S increased by 40% from 2010 to 2016, how many employees were there at skill level T in 2016?

M and N had four children P, Q, R and S. Of them, only P and R were married. They had children X and Y respectively. If Y is a legitimate child of W, which one of the following statements is necessarily FALSE?

Consider the matrix

$\mathrm p=\begin{bmatrix}1&1&0\\0&1&1\\0&0&1\end{bmatrix}$

The number of distinct eigenvalues of P is

A parabola $x=y^2$ with $0\leq x\leq1$ is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by 360° around the x-axis is

For the equation $\frac{\mathrm dy}{\mathrm dx}$ + 7x2 = 0, if (0) = 3/7, then the value of (1) is

The lengths of a large stock of titanium rods follow a normal distribution with a mean $(\mathrm\mu)$ of 440 mm and a standard deviation $(\mathrm\sigma)$ of 1 mm. What is the percentage of rods whose lengths lie between 438 mm and 441 mm?

A flat-faced follower is driven using a circular eccentric cam rotating at a constant angular velocity $\mathrm\omega$. At time t = 0, the vertical position of the follower is (0) = 0, and the system is in the configuration shown below.

The vertical position of the follower face, (t) is given by

The natural frequencies corresponding to the spring-mass systems I and II are ${\mathrm\omega}_{\mathrm I}$ and ${\mathrm\omega}_{\mathrm{II}}$, respectively. The ratio $\frac{{\mathrm\omega}_{\mathrm I}}{{\mathrm\omega}_{\mathrm{II}}}$ is

A spur gear with 20° full depth teeth is transmitting 20 kW at 200 rad/s. The pitch circle diameter of the gear is 100 mm. The magnitude of the force applied on the gear in the radial direction is